# Mathematics Major

The program in Mathematics leads to a degree of Bachelor of Science in Mathematics and offers students training in preparation for graduate work, teaching, and positions in government or industry. Mathematical training is integrated with computer use in several courses. Because a strong mathematical background is important in many fields, over half of UMCP Mathematics majors are double majors. Additional information on these topics and mathematics is available from the departmental website.

## PLACEMENT IN COURSES

The Department of Mathematics has a large offering to accommodate a great variety of background, interests, and abilities. The department permits students to take any course for which they have the appropriate background, regardless of formal course work. For example, students with a high school calculus course may be permitted to begin in the middle of the calculus sequence even if they do not have advanced standing. Students may obtain undergraduate credit for mathematics courses in any of the following ways: passing the appropriate CEEB Advanced Placement Examination, passing standardized CLEP examinations, and through the department's Credit-by-Examination. Students are urged to consult with advisors from the Department of Mathematics to assist with proper placements.

## Program Objectives

The Department of Mathematics educates its majors in a broad range of modern mathematics while instilling in them a strong ability to solve problems, apply mathematics to other areas, and create rigorous mathematical arguments. The program prepares the majors to further their mathematical education in graduate school, or to teach at the secondary school level, or to work in government or business.

## Program Learning Outcomes

- Students will acquire problem-solving skills in a broad range of significant mathematics.
- Students will gain an understanding of what constitutes mathematical thinking, including the ability to produce and judge the validity of rigorous mathematical arguments.
- Students will be able to communicate mathematical ideas and arguments.
- Students will be prepared to use mathematics in their future endeavors, not only in the discipline of mathematics, but also in other disciplines.

### Statistics and Probability and Applied Mathematics

Courses in statistics and probability, and applied mathematics are offered by the Department of Mathematics. These courses are open to non-majors as well as majors, and carry credit in mathematics. Students wishing to concentrate in the above may do so by choosing an appropriate program under the Department of Mathematics.

There are four tracks for the major: the traditional track, the applied mathematics track, the secondary education track, and the statistics track. The secondary education track is for students seeking to become certified to teach mathematics at the secondary level. Each mathematics major must complete each required course with a grade of C- or better and with an overall major GPA of 2.0.

## Traditional Track

Course | Title | Credits |
---|---|---|

Introductory Sequence ^{1} | ||

MATH140 | Calculus I | 4 |

MATH141 | Calculus II | 4 |

MATH240 | Introduction to Linear Algebra | 4 |

MATH241 | Calculus III | 4 |

MATH310 | Introduction to Mathematical Proof | 3 |

Select one of the following: | 3-4 | |

Differential Equations for Scientists and Engineers | ||

Differential Geometry of Curves and Surfaces I | ||

Partial Differential Equations | ||

MATH/AMSC/STAT Courses | ||

Select eight courses of 400-level or higher; must include: ^{2} | ||

MATH410 | Advanced Calculus I | 3 |

Select one of the following: | 3 | |

Applications of Linear Algebra | ||

Introduction to Abstract Algebra | ||

Linear Algebra | ||

Select one of the following: | 3 | |

Computational Methods | ||

or AMSC466 | Introduction to Numerical Analysis I | |

Depth Requirement; a one year sequence chosen from the following: | 6 | |

Advanced Calculus I and Advanced Calculus II | ||

Introduction to Abstract Algebra and Field Theory | ||

Introduction to Abstract Algebra and Linear Algebra | ||

Introduction to Probability Theory and Introduction to Statistics | ||

Electives ^{3, 4} | ||

Select one of the following: ^{5} | 3-4 | |

Introduction to C Programming | ||

Introduction to Computer Programming via the Web | ||

Object-Oriented Programming I | ||

Object-Oriented Programming II | ||

Computing Fundamentals for Engineers | ||

Intermediate Programming Concepts for Engineers | ||

Introduction to Programming in the Physical Sciences | ||

Supporting three-course sequence ^{6} | ||

Select one of eight sequences | 9-13 | |

Sequence One (11 credits) | ||

General Physics: Mechanics and Particle Dynamics | ||

General Physics: Vibration, Waves, Heat, Electricity and Magnetism and General Physics: Vibrations, Waves, Heat, Electricity and Magnetism (Laboratory) | ||

General Physics: Electrodynamics, Light, Relativity and Modern Physics and General Physics: Electrodynamics, Light, Relativity and Modern Physics (Laboratory) | ||

Sequence Two (9 credits) | ||

Introductory Physics: Mechanics and Relativity | ||

Introductory Physics: Fields | ||

Introductory Physics: Waves | ||

Sequence Three (9 credits) | ||

Mechanics I | ||

General Physics: Mechanics and Particle Dynamics | ||

Mechanics II | ||

Sequence Four (12 credits) | ||

Object-Oriented Programming II | ||

Introduction to Computer Systems | ||

Discrete Structures | ||

Sequence Five (13 credits) | ||

Principles of General Chemistry and Introduction to Laboratory Practices and Research in the Chemical Sciences | ||

Principles of Organic Chemistry I | ||

Principles of Organic Chemistry II | ||

Sequence Six (12 credits) | ||

Chemistry I - Fundamentals of General Chemistry and General Chemistry I Laboratory | ||

Organic Chemistry I and Organic Chemistry Laboratory I | ||

Organic Chemistry II and Organic Chemistry Laboratory II | ||

Sequence Seven (11 credits) | ||

Principles of Microeconomics | ||

Principles of Macroeconomics | ||

Intermediate Macroeconomic Theory and Policy | ||

or ECON306 | Intermediate Microeconomic Theory & Policy | |

Sequence Eight (9 credits) | ||

Principles of Accounting I | ||

Principles of Accounting II | ||

Business Finance | ||

Total Credits | 49-55 |

^{1} | Or honors sequence: MATH340-MATH341.Completion of MATH340 satisfies the requirement for MATH241; completion of MATH340-MATH341 satisfies the requirement for MATH240-MATH241-MATH246. |

^{2} | At least four courses must be taken at College Park. |

^{3} | 400 level courses. Students with a strong interest in applied mathematics may, with the approval of the Undergraduate Office, substitute two courses (with strong mathematics content) from outside the Mathematics Department for one upper-level elective course. |

^{4} | May not include: MATH400, MATH461, MATH478, MATH480-MATH484, STAT464 |

^{5} | A student may be exempt from this requirement if (s)he can demonstrate adequate programming knowledge from prior course or work experience. |

^{6} | Intended to broaden the student's mathematical experience. (Other sequences might be approved by the Undergraduate Office but they would have to make use of mathematical ideas, comparable to the sequences on this list.) |

## Applied Mathematics Track

Course | Title | Credits |
---|---|---|

Introductory Sequence ^{1} | ||

MATH140 | Calculus I ^{1} | 4 |

MATH141 | Calculus II | 4 |

MATH240 | Introduction to Linear Algebra | 4 |

MATH241 | Calculus III | 4 |

MATH310 | Introduction to Mathematical Proof | 3 |

Select one of the following: | 3 | |

Differential Equations for Scientists and Engineers | ||

Differential Geometry of Curves and Surfaces I | ||

Partial Differential Equations | ||

MATH/AMSC/STAT Courses | ||

Select eight 400-level or higher; must include: ^{2} | ||

MATH410 | Advanced Calculus I | 3 |

STAT410 | Introduction to Probability Theory | 3 |

STATXXX | One additional STAT course other than STAT400, STAT410, STAT464 | 3 |

MATH401 | Applications of Linear Algebra | 3 |

or MATH405 | Linear Algebra | |

AMSC460 | Computational Methods | 3 |

or AMSC466 | Introduction to Numerical Analysis I | |

Select one of the following: | 3 | |

Applied Harmonic Analysis: An Introduction to Signal Processing | ||

Mathematical Modeling | ||

Introduction to the Mathematics of Finance | ||

Geometry for Computer Applications | ||

Introduction to Dynamics and Chaos | ||

Cryptography | ||

Partial Differential Equations | ||

Transform Methods for Scientists and Engineers | ||

Combinatorics and Graph Theory | ||

Depth Requirement; a one year sequence chosen from the following: | 6 | |

Advanced Calculus I and Advanced Calculus II | ||

Applied Harmonic Analysis: An Introduction to Signal Processing and Transform Methods for Scientists and Engineers | ||

Electives ^{3, 4} | ||

Select one of the following: ^{5} | ||

Introduction to C Programming | ||

Introduction to Computer Programming via the Web | ||

Object-Oriented Programming I | ||

Object-Oriented Programming II | ||

Computing Fundamentals for Engineers | ||

Intermediate Programming Concepts for Engineers | ||

Introduction to Programming in the Physical Sciences | ||

Supporting Three-course Sequence ^{6} | ||

Select one of twelve sequences | 9-13 | |

Sequence One (11 credits) | ||

General Physics: Mechanics and Particle Dynamics | ||

General Physics: Vibration, Waves, Heat, Electricity and Magnetism and General Physics: Vibrations, Waves, Heat, Electricity and Magnetism (Laboratory) | ||

General Physics: Electrodynamics, Light, Relativity and Modern Physics and General Physics: Electrodynamics, Light, Relativity and Modern Physics (Laboratory) | ||

Sequence Two (9 credits) | ||

Introductory Physics: Mechanics and Relativity | ||

Introductory Physics: Fields | ||

Introductory Physics: Waves | ||

Sequence Three (9 credits) | ||

Mechanics I | ||

General Physics: Mechanics and Particle Dynamics | ||

Mechanics II | ||

Sequence Four (12 credits) | ||

Object-Oriented Programming II | ||

Introduction to Computer Systems | ||

Discrete Structures | ||

Sequence Five (13 credits) | ||

Principles of General Chemistry and Introduction to Laboratory Practices and Research in the Chemical Sciences | ||

Principles of Organic Chemistry I | ||

Principles of Organic Chemistry II | ||

Sequence Six (12 credits) | ||

Chemistry I - Fundamentals of General Chemistry and General Chemistry I Laboratory | ||

Organic Chemistry I and Organic Chemistry Laboratory I | ||

Organic Chemistry II and Organic Chemistry Laboratory II | ||

Sequence Seven (11 credits) | ||

Principles of Microeconomics | ||

Principles of Macroeconomics | ||

Intermediate Macroeconomic Theory and Policy | ||

or ECON306 | Intermediate Microeconomic Theory & Policy | |

OR | ||

Intermediate Macroeconomic Analysis | ||

or ECON326 | Intermediate Microeconomic Analysis | |

Sequence Eight (9 credits) | ||

Principles of Accounting I | ||

Principles of Accounting II | ||

Business Finance | ||

Sequence Nine (12-13 credits) | ||

Principles of Molecular & Cellular Biology and Principles of Molecular & Cellular Biology Laboratory | ||

Principles of Ecology and Evolution and Principles of Ecology and Evolution Lab | ||

Chemistry I - Fundamentals of General Chemistry and General Chemistry I Laboratory | ||

OR | ||

Principles of General Chemistry and Introduction to Laboratory Practices and Research in the Chemical Sciences | ||

Sequence Ten (10 credits) | ||

Introductory Astrophysics - Solar System | ||

Introductory Astrophysics II - Stars and Beyond | ||

General Physics: Mechanics and Particle Dynamics | ||

or PHYS171 | Introductory Physics: Mechanics and Relativity | |

Sequence Eleven (12 credits) | ||

Physical Geology and | ||

Select Two From: | ||

Mineralogy | ||

Geomorphology | ||

Structural Geology | ||

Introduction to the Blue Ocean | ||

Sequence Twelve (10 credits) | ||

Weather and Climate and Weather and Climate Laboratory | ||

Two additional 400-level AOSC courses | ||

Total Credits | 55-59 |

^{1} | Or honors sequence: MATH340-MATH341.Completion of MATH340 satisfies the requirement for MATH241; completion of MATH340-MATH341 satisfies the requirement for MATH240-MATH241-MATH246. |

^{2} | At least four courses must be taken at College Park. |

^{3} | 400 level courses. May not include: MATH400, MATH461, MATH478, MATH480-MATH484, STAT464 |

^{4} | |

^{5} | A student may be exempt from this requirement if (s)he can demonstrate adequate programming knowledge from prior course or work experience. |

^{6} | Intended to broaden the student's mathematical experience. (Other sequences might be approved by the Undergraduate Office but they would have to make use of mathematical ideas, comparable to the sequences on this list. |

## Secondary Education Track

Course | Title | Credits |
---|---|---|

Introductory Sequence ^{1} | ||

MATH140 | Calculus I | 4 |

MATH141 | Calculus II | 4 |

MATH240 | Introduction to Linear Algebra | 4 |

MATH241 | Calculus III | 4 |

MATH310 | Introduction to Mathematical Proof | 3 |

Select one of the following: | 3-4 | |

Differential Equations for Scientists and Engineers | ||

Multivariable Calculus, Linear Algebra, Differential Equations II (Honors) | ||

Applications of Linear Algebra | ||

Mathematical Modeling | ||

Introduction to Dynamics and Chaos | ||

Partial Differential Equations | ||

Computational Methods | ||

Introduction to Numerical Analysis I | ||

MATH/AMSC/STAT Courses ^{2} | ||

Select seven courses at the 400-level or higher, must include: | ||

MATH410 | Advanced Calculus I | 3 |

MATH430 | Euclidean and Non-Euclidean Geometries | 3 |

MATH402 | Algebraic Structures | 3 |

or MATH403 | Introduction to Abstract Algebra | |

STAT400 | Applied Probability and Statistics I | 3 |

or STAT410 | Introduction to Probability Theory | |

Select one of the following: | 3 | |

Introduction to Number Theory | ||

Elementary Mathematical Logic | ||

Axiomatic Set Theory | ||

Cryptography | ||

Combinatorics and Graph Theory | ||

Electives 400-level MATH/AMSC/STAT course ^{3} | ||

Select one of the following: ^{4} | 3-4 | |

Introduction to C Programming | ||

Introduction to Computer Programming via the Web | ||

Object-Oriented Programming I | ||

Object-Oriented Programming II | ||

Computing Fundamentals for Engineers | ||

Intermediate Programming Concepts for Engineers | ||

Education Requirements ^{5} | ||

PHYS165 | Introduction to Programming in the Physical Sciences | 3 |

EDCI450 | Internship Seminar in Secondary Education: Mathematics | 1 |

EDCI451 | 12 | |

Supporting Sequence ^{6} | ||

Select one of six sequences | 7-8 | |

Sequence One (8 credits) | ||

Chemistry I - Fundamentals of General Chemistry and General Chemistry I Laboratory | ||

Organic Chemistry I and Organic Chemistry Laboratory I | ||

Sequence Two (7 credits) | ||

General Physics: Mechanics and Particle Dynamics | ||

General Physics: Vibration, Waves, Heat, Electricity and Magnetism and General Physics: Vibrations, Waves, Heat, Electricity and Magnetism (Laboratory) | ||

Sequence Three (8 credits) | ||

Principles of Molecular & Cellular Biology and Principles of Molecular & Cellular Biology Laboratory | ||

Principles of Ecology and Evolution and Principles of Ecology and Evolution Lab | ||

Sequence Four (7 credits) | ||

Introductory Astrophysics - Solar System | ||

Introductory Astrophysics II - Stars and Beyond | ||

Sequence Five (7-8 credits) | ||

Physical Geology and Physical Geology Laboratory | ||

Mineralogy | ||

or GEOL340 | Geomorphology | |

or GEOL341 | Structural Geology | |

or GEOL375 | Introduction to the Blue Ocean | |

Sequence Six (7 credits) | ||

Weather and Climate and Weather and Climate Laboratory | ||

AOSC4xx Any 400 level AOSC course | ||

Total Credits | 63-66 |

^{1} | Or honors sequence: MATH340-MATH341.Completion of MATH340 satisfies the requirement for MATH241; completion of MATH340-MATH341 satisfies the requirement for MATH240-MATH241-MATH246. |

^{2} | At least four courses must be taken at College Park. |

^{3} | may not include: MATH400, MATH461,MATH478, MATH480-MATH484, or STAT464 |

^{4} | A student may be exempt from this requirement if (s)he can demonstrate adequate programming knowledge from prior course or work experience |

^{5} | The student-teaching pair EDCI450-EDCI451 is 13 credits and has further prerequisites in the College of Education. In order to take these courses the student must be admitted into the College of Education. A student in the secondary education track of the mathematics major would normally be expected to receive a double major in Mathematics and Mathematics Education. |

^{6} | These are intended to broaden the student's mathematical experience. (Other sequences might be approved by the Undergraduate Office but they would have to make use of mathematical ideas, comparable to the sequences on this list. |

## Statistics Track

Course | Title | Credits |
---|---|---|

Introductory Sequence ^{1} | ||

MATH140 | Calculus I | 4 |

MATH141 | Calculus II | 4 |

MATH240 | Introduction to Linear Algebra | 4 |

MATH241 | Calculus III | 4 |

MATH310 | Introduction to Mathematical Proof | 3 |

Select one of the following: | 3 | |

Differential Equations for Scientists and Engineers | ||

Differential Geometry of Curves and Surfaces I | ||

Partial Differential Equations | ||

MATH/AMSC/STAT Courses ^{2} | ||

Select eight courses, must include: | ||

MATH410 | Advanced Calculus I | 3 |

STAT410 | Introduction to Probability Theory | 3 |

STAT430 | Introduction to Statistical Computing with SAS | 3 |

AMSC460 | Computational Methods | 3 |

or AMSC466 | Introduction to Numerical Analysis I | |

MATH401 | Applications of Linear Algebra | 3 |

or MATH405 | Linear Algebra | |

STAT401 | Applied Probability and Statistics II | 3 |

or STAT420 | Introduction to Statistics | |

Select two of the following: | 6 | |

STAT4xx | Any 400-level or higher STAT courses ^{3} | |

Advanced Calculus II | ||

Introduction to the Mathematics of Finance | ||

Transform Methods for Scientists and Engineers | ||

Select one of the following: ^{4} | 3-4 | |

Introduction to C Programming | ||

Introduction to Computer Programming via the Web | ||

Object-Oriented Programming I | ||

Object-Oriented Programming II | ||

Computing Fundamentals for Engineers | ||

Intermediate Programming Concepts for Engineers | ||

Introduction to Programming in the Physical Sciences | ||

Supporting Three-course Sequence ^{5} | ||

Select one of eight sequences | 9-13 | |

Sequence One (11 credits) | ||

General Physics: Mechanics and Particle Dynamics | ||

General Physics: Vibration, Waves, Heat, Electricity and Magnetism and General Physics: Vibrations, Waves, Heat, Electricity and Magnetism (Laboratory) | ||

General Physics: Electrodynamics, Light, Relativity and Modern Physics and General Physics: Electrodynamics, Light, Relativity and Modern Physics (Laboratory) | ||

Sequence Two (9 credits) | ||

Introductory Physics: Mechanics and Relativity | ||

Introductory Physics: Fields | ||

Introductory Physics: Waves | ||

Sequence Three (9 credits) | ||

Mechanics I | ||

General Physics: Mechanics and Particle Dynamics | ||

Mechanics II | ||

Sequence Four (12 credits) | ||

Object-Oriented Programming II | ||

Introduction to Computer Systems | ||

Discrete Structures | ||

Sequence Five (13 credits) | ||

Principles of General Chemistry and Introduction to Laboratory Practices and Research in the Chemical Sciences | ||

Principles of Organic Chemistry I | ||

Principles of Organic Chemistry II | ||

Sequence Six (12 credits) | ||

Chemistry I - Fundamentals of General Chemistry and General Chemistry I Laboratory | ||

Organic Chemistry I and Organic Chemistry Laboratory I | ||

Organic Chemistry II and Organic Chemistry Laboratory II | ||

Sequence Seven (11 credits) | ||

Principles of Microeconomics | ||

Principles of Macroeconomics | ||

Intermediate Macroeconomic Theory and Policy | ||

or ECON306 | Intermediate Microeconomic Theory & Policy | |

Sequence Eight (9 credits) | ||

Principles of Accounting I | ||

Principles of Accounting II | ||

Business Finance | ||

Total Credits | 58-63 |

^{1} | |

^{2} | At least four courses must be taken at College Park. |

^{3} | except STAT464 |

^{4} | A student may be exempt from this requirement if (s)he can demonstrate adequate programming knowledge from prior course or work experience |

^{5} | Intended to broaden the student's mathematical experience. (Other sequences might be approved by the Undergraduate Office but they would have to make use of mathematical ideas comparable to the sequences on this list.) |

## Other Requirements for the Major

### Areas of Study

Within the Department of Mathematics there are a number of identifiable areas which students can pursue to suit their own goals and interests. They are briefly described below. Note that they do overlap and that students need not confine themselves to one of them.

#### 1. Pure Mathematics

Courses that belong to this area include:

Course | Title | Credits |
---|---|---|

MATH402 | Algebraic Structures | 3 |

MATH403 | Introduction to Abstract Algebra | 3 |

MATH404 | Field Theory | 3 |

MATH405 | Linear Algebra | 3 |

MATH406 | Introduction to Number Theory | 3 |

MATH410 | Advanced Calculus I | 3 |

MATH411 | Advanced Calculus II | 3 |

MATH430 | Euclidean and Non-Euclidean Geometries | 3 |

MATH432 | Introduction to Topology | 3 |

MATH436 | Differential Geometry of Curves and Surfaces I | 3 |

MATH437 | Differential Forms | 3 |

MATH445 | Elementary Mathematical Logic | 3 |

MATH452 | Introduction to Dynamics and Chaos | 3 |

MATH456 | Cryptography | 3 |

STAT410 | Introduction to Probability Theory | 3 |

STAT420 | Introduction to Statistics | 3 |

Students preparing for graduate school in mathematics should include: | ||

MATH403 | Introduction to Abstract Algebra | 3 |

MATH405 | Linear Algebra | 3 |

MATH410 | Advanced Calculus I | 3 |

MATH411 | Advanced Calculus II | 3 |

MATH463 | Complex Variables for Scientists and Engineers | 3 |

or MATH660 | Complex Analysis I | |

MATH432 | Introduction to Topology (is also desirable) | 3 |

or MATH730 | Fundamental Concepts of Topology |

Other courses from the above list and graduate courses are also appropriate.

#### 2. Secondary Teaching

In addition to the courses required by the Secondary Education Track, the following courses are particularly suited for students preparing to teach:

Course | Title | Credits |
---|---|---|

MATH401 | Applications of Linear Algebra | 3 |

MATH406 | Introduction to Number Theory | 3 |

MATH445 | Elementary Mathematical Logic | 3 |

MATH470 | Mathematics for Secondary Education | 3 |

MATH475 | Combinatorics and Graph Theory | 3 |

Students who are interested in secondary teaching should contact also the College of Education for certification requirements and other information: www.education.umd.edu/studentinfo.

#### 3 .Statistics

For a student with a Bachelor's degree seeking work requiring some statistical background, the minimal program is STAT400-STAT401. To work primarily as a statistician, one should combine STAT400-STAT401 with STAT430 and at least one more statistics course, most suitably, STAT440. A deeper sequence is STAT410, STAT420, STAT430. This offers a better understanding and wider knowledge of statistics and is a general purpose program (i.e., does not specify one area of application). For economics applications,

MATH424, STAT400, STAT401, STAT430, STAT440 should be considered. To prepare for graduate work, STAT410 and STAT420 give the best background, with STAT430, STAT440 added at some later stage.

#### 4. Computational Mathematics

There are a number of math courses which emphasize the computational aspects of mathematics including the use of the computer. They are:

Course | Title | Credits |
---|---|---|

AMSC460 | Computational Methods | 3 |

AMSC466 | Introduction to Numerical Analysis I | 3 |

MATH431 | Geometry for Computer Applications | 3 |

MATH456 | Cryptography | 3 |

MATH475 | Combinatorics and Graph Theory | 3 |

STAT430 | Introduction to Statistical Computing with SAS | 3 |

Students interested in this area should take the CMSC supporting sequence as soon as possible.

#### 5. Applied Mathematics

The courses that lead most rapidly to applications are the courses listed above in 3 and 4 and

Course | Title | Credits |
---|---|---|

MATH401 | Applications of Linear Algebra | 3 |

MATH416 | Applied Harmonic Analysis: An Introduction to Signal Processing | 3 |

MATH420 | Mathematical Modeling | 3 |

MATH452 | Introduction to Dynamics and Chaos | 3 |

MATH462 | Partial Differential Equations | 3 |

MATH464 | Transform Methods for Scientists and Engineers | 3 |

A student interested in applied mathematics should obtain, in addition to a solid training in mathematics, a good knowledge of at least one area in which mathematics is currently being applied. Concentration in this area is good preparation for employment in government and industry or for graduate study in applied mathematics.

Click here for roadmaps for four-year plans in the College of Computer, Mathematical, and Natural Sciences.

Additional information on developing a four-year academic plan can be found on the following pages:

- 4yearplans.umd.edu
- the Student Academic Success-Degree Completion Policy section of this catalog